The upbeat sentiment supported the euro and dollar against the yen, while the Japanese unit was also pressured by news that the country suffered a record current account deficit in January.
Tokyo gained 1.27 percent by the break, Hong Kong was 0.65 percent higher, Sydney put on 0.52 percent, Shanghai rose 0.75 percent and Seoul added 0.39 percent.
The previous day's nervousness over Greece's deal was all but gone after it emerged Wednesday that more than half its creditors had agreed to join in the operation, which will see them write off 107-billion euros ($141 billion) in debt.
The success of the plan is a crucial part of a 237-billion-euro second bailout for Athens, which is aimed at preventing the country from defaulting on its obligations, a move that could spark another global downturn.
The upward momentum was supported by news that the US private sector added a net 216,000 jobs in February, following a slightly upwardly revised 173,000 reading for January.
The data from payrolls firm ADP are the latest in a string of positive jobs figures in the United States that point to a gradual improvement in the world's number-one economy.
It also lifted hopes for crucial non-farm payroll results that are due on Friday and which analysts will be keenly looking at for an indication of the strength of the recovery.
In January, the unemployment rate fell for the fifth straight month, to 8.3 percent, the lowest level since February 2009.
"If last night's optimism on the (Greek swap deal) is confirmed and US non-farm payrolls follow the ADP data on (Friday), expect the momentum the market had at the beginning of the year to continue," Miguel Audencial, sales trader at CMC Markets, said in a note.
"On the other hand if it's double bogey where both provide unsatisfying results, anticipate more fear to be displayed by the equity market," he added, according to Dow Jones Newswires.
On currency markets the euro stood at $1.3141 and 106.75 yen, compared with $1.3148 and 106.67 late Wednesday in New York.
The yen retreated after Japan reported the deficit in the current account, the broadest measure of trade with the rest of the world, stood at 437.3 billion yen ($5.4 billion) in January, due to lower exports and higher energy costs.
It was the first deficit since January 2009 when Japan registered its previous record shortfall of 132.7 billion yen at the height of the global downturn.
The yen stood at 81.29 to the dollar in morning trade in Tokyo, slipping from 81.03 in New York.
Oil prices were flat, with reports of a rise in stockpiles in the United States tempering supplies fears caused by the ongoing nuclear row between Iran and the West.
New York's main contract, light sweet crude for April delivery, fell a cent to $106.15 and Brent North Sea crude for delivery in April shed two cents to $124.10.
Gold was at $1,686.40 an ounce at 0330 GMT, compared with $1,681.40 late Wednesday.
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